Data compression is used for a wide variety of applications (e.g., image sensing and processing, wireless/wireline communications, internet communications, etc.) to improve the bandwidth usage, speed, quality, noise reduction, and other parameters of the particular application. A key factor for efficient data compression is reducing the number of coefficients of the basis function for the signal transform used to represent the original data signals where the coefficients are associated (related to) with vectors of the digital signal transform matrix. The coefficients are used to reconstruct (recover) the original data signals and therefore reducing the number of coefficients (needed for signal reconstruction) to a minimum number (top coefficients) leads to a reduction in the digital signal processing (DSP) computational requirements for reconstructing (recover) the original digital signal, and therefore improves the efficiency of the data compression method (technique) while maintaining a reasonably low error rate.
A number of data compression techniques are currently used to improve efficiency (and reduce errors) which use different signal representation transforms wherein examples include Discrete Fourier transform (DFT), Fast Fourier transform (FFT), and wavelet-based transforms (e.g., discrete wavelet transform-DWT). However, the DSP computational complexity using DFTs may be still relatively high as compared to FFTs or wavelet-based transforms. For example, where N is the sample length of an input data signal (e.g., N=512) or size of an input image (e.g., N=65,536 for an input image of size 256×256), the computational complexity for the DFT is N2 (e.g., N2 =262,144 for an input data signal of length 512, or N232 [65,536]2 for an input image of size 256×256). Also, DFTs and FFTs use a sine or cosine function (basis function) which may be less accurate for certain signal representations (e.g., signals with discontinuity) and thus makes wavelet-based transforms (using wavelets—small, localized waves or waveforms) a better data compression choice for many communications systems. Additionally, communications systems using wavelet-based transforms (wavelet modulation) as part of an orthogonal frequency division multiplexing (OFDM) service offering may provide a number of advantages including greater stop-band separation (e.g., more than 40 dB separation as compared to other modulation techniques) leading to greater resistance to noise and interference and more channels, easier equalization, better feature extraction, less need for external filters, and more efficient spectral utilization.
However, although wavelet-based compression offers many advantages over other data compression techniques, there is still a problem for wavelet-based transforms of finding the best, orthogonal basis function (and minimum number of coefficients of the best basis function) of the digital signal transform used to represent the original imaging data signal. For example, DWT only uses a specific basis function (wavelet basis function) out of the large plurality (e.g., thousands) of possible (orthogonal) basis functions available from an associated wavelet packet dictionary.
A commonly-used method for finding the best basis function (base) for wavelet packet applications (e.g., WPD) is the binary-tree best base searching method (BTBB) which is based on wavelet theory that if a orthonormal wavelet filter pair is used, coefficients at the same decomposition level are orthogonal to each other, and also coefficients in a parent node are orthogonal to all the coefficients at one level down except for the coefficients at its children nodes. From this theory, the BTBB method finds the best orthogonal base (basis function) by exclusively selecting base vectors from either a parent node or its directly-related children nodes in the binary-tree structure based on a group cost measurement (e.g., comparing the entropy of the parent node to the entropy of the children nodes).
However, exclusively selecting base vectors from only the parent node or only its children nodes is a limitation on the set of available orthogonal bases since many vectors in the children node may be orthogonal to the vectors in its parent node. Thus, the BTBB method only searches within a limited sub-set of the set containing all of the orthogonal bases in the associated wavelet packet dictionary.
Therefore, due to the disadvantages of the current best base searching methods for wavelet-based applications, there is a need to provide a method and system which determines the best orthogonal basis function (base) by searching a set of bases including (approximately) all orthogonal bases available to provide the minimum number of coefficients for efficient, wavelet-based image data compression while maintaining a low error rate in reconstructing the original data signals.